12 Tones with M12
Sequence
Permutation
C
V
B
N
M
,
.
F
G
J
K
L
The sporadic simple Mathieu group M12 acts as permutations on any set with 12 elements, e.g. the 12 tones of the chromatic scale. In fact it acts simply 5-transitively, which means that, for any 5 tones you choose, in any order, M12 has in mind a specific completion of that sequence, to a full sequence of 12 tones. This app lets you hear those tones: Use the keyboard to enter 5 distinct tones, and it will respond with 7 tones that complete your sequence, as dictated by M12. (It'll also show you the permutation in M12 that defines the complete sequence.)
N.B. There are many copies of M12 in the full symmetric group of degree 12, which means there are different ways that M12 can act on 12 tones. The sequence completions you get from this app depend upon the specific copy we chose (viz. the one you get from GAP) to generate the code.
This app uses web audio. Click "Start" or press Enter to enable audio and begin.